Local Log-empirical Likelihood Inference for Varying-coefficient Density-ratio Models Based on Case-control Data

Abstract

[evdate 2013-12-19] HKUST International Forum on Probability and Statistics. Talk no.20. Title from slide title.

The Second HKUST International Forum on Probability and Statistics (2013), held 19 December, 2013, at the Hong Kong University of Science and Technology. Co-sponsored by the HKUST Jockey Club Institute for Advanced Study and the Center for Statistical Science.

'Joint with Dr. Xu Liu and Dr. Hongmei Jiang.'

Abstract: Treatment effect is an important index in comparing two-sample data in survival analysis, industry manufacture, clinical medicine and many other applications. The speaker propose a unified semiparametric approach to estimate different types of treatment effects under a case-control sampling plan with the logistic regression model assumption, which is equivalent to a two-sample density ratio model. For different treatment effects, the speaker constructs different estimating functions and the nuisance parameters in estimating functions are estimated firstly by the empirical likelihood method. Here, the talk allows that the functions are nonsmooth with respect to parameters. The confidence interval for the treatment effect based on the empirical likelihood ratio method is also presented. The talk proves that the estimator based on the estimating equation is consistent and asymptotically normal and the empirical log-likelihood ratio statistic has a limiting scaled chi-square distribution. Simulation studies are reported to assess the finite sample properties of the proposed estimator and the performance of the confidence interval. The proposed methods are applied to real data examples and some interesting results are presented.

Duration: 32 min.